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Fight fire with fire. (Lugia against Lugia)

Look at his weaknesses! Darkrai can use Dark Void + Calm Mind a few times then things like Dark Pulse and Thunderbolt should OHKO him. EDIT: Did some stat calcs and Calm Mind 3 times plus Dark Gem plus Dark Pulse = OHKO

Wobbufet with Destiny Bond (LOL) {Not too reliable}

Zekrom can dominate as well with Thunder Wave then Hone Claws 3 times. Follow it with Bolt Strike for an OHKO. (Tested)

Giratina with Shadow Force is Super Effective. Plus Toxic! (Tested and equals 1-2 hits for KO)
Those are only a few.
I have never seen Lugia as a huge force, so sorry if this didn't help.